Uniform approximation by □b-harmonic functions

Abstract

The Mergelyan and Ahlfors-Beurling estimates for the Cauchy transform give quantitative information on uniform approximation by rational functions with poles off K . We will present an analogous result for an integral transform on the unit sphere in C 2 introduced by Henkin, and show how it can be used to study approximation by functions that are locally harmonic with respect to the Kohn Laplacian 2 b .